等差:an+a(n+1)=2bn,即an/bn+a(n+1)/bn=2
等比:bnb(n+1)=a(n+1)^2,即a(n+1)/bn=b(n+1)/a(n+1)
代入得:an/bn+b(n+1)/a(n+1)=2
令cn=an/bn,c1=1/2
上式即:cn+1/c(n+1)=2
化为:1/[1-c(n+1)]=1/(1-cn)+1
令dn=1/(1-cn),所以dn 为等差数列,首项d1=2.q=1
dn=1/(1-cn)=d1+n-1=n+1
cn=1-1/(n+1)=n/(n+1)